Abstract: A mathematical model and the differential equations of the motion of the hanging high speed bogie with hysteretic nonlinearity are established in this paper. The stability theory of ordinary differential equations is applied to the analysis the hunting movement of the bogie. Meanwhile, the method of statistic linearization is adopted to handle the nonlinear equations. As a result, the sufficient conditions to prevent hunting movements are identified. The influence of the design parameters of bogie on its critical speed is also studied in order to provide the basis for design.